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Tetrahedron OABC with minimal perimeter

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September 22, 2010
geometry3D geometrytetrahedronperimeterminimizationIMO Shortlist

Problem Statement

Let Ox,Oy,OzOx, Oy, Oz be three rays, and GG a point inside the trihedron OxyzOxyz. Consider all planes passing through GG and cutting Ox,Oy,OzOx, Oy, Oz at points A,B,CA,B,C, respectively. How is the plane to be placed in order to yield a tetrahedron OABCOABC with minimal perimeter ?
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